Finite Group Databasebeta

← Group #512067

Character table — Group #512067

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222222444488882222244444488884444444444444444888881616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111
χ611111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1
χ811111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ9111111-1-111111111-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ10111111-1-111111111-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-111-11-11
χ11111111-1-111111111-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-111-1-11111-1-1-1-111-1-1-11-11
χ12111111-1-111111111-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-111-1-1-1-1-1-11111-1-1111-11-1
χ13111111-1-111111111-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-111-111-1
χ14111111-1-111111111-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-1-11-1-11
χ15111111-1-111111111-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ16111111-1-111111111-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1
χ17222222222222-2-2-2-222222222222-2-2-2-20000000000000000-2-2-2-2-20000000000000000
χ18222222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-222220000000000000000
χ19222222-2-22222-2-2-2-2-222-2-2-2-222-2-222-2-200000000000000002-2-2220000000000000000
χ20222222-2-22222-2-2-2-2-2-2-222-2-2-2-22222-2-20000000000000000222-2-20000000000000000
χ212222-2-2222-2-222222-200002-2000022-2-22222-2-2-2-200000000-200000000000000000000
χ222222-2-2222-2-222222-200002-2000022-2-2-2-2-2-2222200000000-200000000000000000000
χ232222-2-2222-2-22-2-2-2-2-200002-20000-2-2220000000022-2-222-2-2200000000000000000000
χ242222-2-2222-2-22-2-2-2-2-200002-20000-2-22200000000-2-222-2-222200000000000000000000
χ252222-2-222-222-20000-22222-22-2-2-2-2000000000000000000000000022−2−222−2−22−22−20000
χ262222-2-222-222-20000-22222-22-2-2-2-20000000000000000000000000−2−222−2−222−22−220000
χ272222-2-222-222-20000-2-2-2-2-2-222222000000000000000000000000022−2−222−2−2−22−220000
χ282222-2-222-222-20000-2-2-2-2-2-2222220000000000000000000000000−2−222−2−2222−22−20000
χ292222-2-2-2-22-2-22222220000-220000-2-2-2-222-2-2-2-22200000000200000000000000000000
χ302222-2-2-2-22-2-22222220000-220000-2-2-2-2-2-22222-2-200000000200000000000000000000
χ312222-2-2-2-22-2-22-2-2-2-220000-22000022220000000022-2-2-2-222-200000000000000000000
χ322222-2-2-2-22-2-22-2-2-2-220000-220000222200000000-2-22222-2-2-200000000000000000000
χ332222-2-2-2-2-222-20000222-2-22-2-2-222000000000000000000000000022−2−2−2−2222−2−220000
χ342222-2-2-2-2-222-20000222-2-22-2-2-2220000000000000000000000000−2−22222−2−2−222−20000
χ352222-2-2-2-2-222-200002-2-2222-222-2-2000000000000000000000000022−2−2−2−222−222−20000
χ362222-2-2-2-2-222-200002-2-2222-222-2-20000000000000000000000000−2−22222−2−22−2−220000
χ3722-2-22-200-22-2222-2-20002-200002-2002-2002i−2i002i−2i2i−2i2i−2i00000002-20000000000000000
χ3822-2-22-200-22-2222-2-20002-200002-2002-200−2i2i00−2i2i−2i2i−2i2i00000002-20000000000000000
χ3922-2-22-200-22-2222-2-2000-220000-22002-2002i−2i002i−2i−2i2i−2i2i0000000-220000000000000000
χ4022-2-22-200-22-2222-2-2000-220000-22002-200−2i2i00−2i2i2i−2i2i−2i0000000-220000000000000000
χ4122-2-22-200-22-22-2-2220002-200002-200-222i−2i002i−2i0000002i−2i2i−2i000-220000000000000000
χ4222-2-22-200-22-22-2-2220002-200002-200-22−2i2i00−2i2i000000−2i2i−2i2i000-220000000000000000
χ4322-2-22-200-22-22-2-222000-220000-2200-222i−2i002i−2i000000−2i2i−2i2i0002-20000000000000000
χ4422-2-22-200-22-22-2-222000-220000-2200-22−2i2i00−2i2i0000002i−2i2i−2i0002-20000000000000000
χ4522-2-2-2200-2-22222-2-202-200002-20000-22002i−2i00−2i2i00002i−2i−2i2i02-2000000000000000000
χ4622-2-2-2200-2-22222-2-202-200002-20000-2200−2i2i002i−2i0000−2i2i2i−2i02-2000000000000000000
χ4722-2-2-2200-2-22222-2-20-220000-220000-22002i−2i00−2i2i0000−2i2i2i−2i0-22000000000000000000
χ4822-2-2-2200-2-22222-2-20-220000-220000-2200−2i2i002i−2i00002i−2i−2i2i0-22000000000000000000
χ4922-2-2-2200-2-222-2-22202-200002-200002-22i−2i00−2i2i002i−2i−2i2i00000-22000000000000000000
χ5022-2-2-2200-2-222-2-22202-200002-200002-2−2i2i002i−2i00−2i2i2i−2i00000-22000000000000000000
χ5122-2-2-2200-2-222-2-2220-220000-2200002-22i−2i00−2i2i00−2i2i2i−2i000002-2000000000000000000
χ5222-2-2-2200-2-222-2-2220-220000-2200002-2−2i2i002i−2i002i−2i−2i2i000002-2000000000000000000
χ5344444444-4-4-4-4000040000-4-4000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000-4000044000000000000000000000000000000000000000000000
χ5544-4-44-4004-44-4000004-40000-440000000000000000000000000000000000000000000
χ5644-4-44-4004-44-400000-4400004-40000000000000000000000000000000000000000000
χ5744-4-4-440044-4-400000004-40000-4400000000000000000000000000000000000000000
χ5844-4-4-440044-4-40000000-4400004-400000000000000000000000000000000000000000
χ594-4-44004-4000022−2222−220000000000022−2200000000000000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000
χ604-4-44004-4000022−2222−220000000000022−2200000000000000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000
χ614-4-44004-40000−2222−222200000000000−222200000000000000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000
χ624-4-44004-40000−2222−222200000000000−222200000000000000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000
χ634-4-4400-44000022−2222−2200000000000−222200000000000000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000
χ644-4-4400-44000022−2222−2200000000000−222200000000000000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000
χ654-4-4400-440000−2222−22220000000000022−2200000000000000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000
χ664-4-4400-440000−2222−22220000000000022−2200000000000000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000
χ678-88-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-88-800000000−424242−420000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.